Application of the contour Minkowski tensor and D statistic to the Planck E -mode data

We test the statistical isotropy (SI) of the $E$-mode polarization of the cosmic microwave background (CMB) radiation observed by the Planck satellite using two statistics, namely, the $\ensuremath{\alpha}$ estimator that is derived from the contour Minkowski tensor (CMT), and the directional statistic ($\mathcal{D}$ statistic). The $\ensuremath{\alpha}$ estimator provides information about the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $\mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. We compute $\ensuremath{\alpha}$ and $\mathcal{D}$ statistic for the low resolution component separated SMICA $E$-mode map of CMB polarization, and compare with the values calculated using FFP10 SMICA simulations. We find good agreement between the Planck data and SMICA simulations for both $\ensuremath{\alpha}$ estimator and $\mathcal{D}$ statistic.